The trans for my 10 is probably very different than the 6. But I also had issues with the "clunkiness" of the trans early on in the break in period. My 10 had this annoying issue where when you would down shift from 3rd on down you would have some slop in the shift lever. What I mean by slop is that you perform the downshift but when your foot comes up and back down on the lever, the lever just drops a bit without any resistance. I have to take my foot back off the lever again before I feel the resistance I should feel and can shift down again. The upshifts were ok but did require some effort. It caused me to grind into 6th once. But ever since clearing the 1000 mile break in period, the bike has shifted beautifully. The slop in the shift lever on downshifts hasn't made itself known lately. The shifts require very little effort now and also with very little travel.
With the neutral issue, I either just come to a complete stop and just pull up on the shift lever to get neutral. The positive neutral finder (or whatever Kawi calls it) is on your 6 too. The way the system is designed you can only get into neutral from first if the bike is completely stopped--regardless of how high you flick up on the shift lever. If you don't want to do this, I find that going all the way down to first and the gradually lift up on the shift lever until the neutral light comes on. Neutral on my bike is very easy to miss when moving. I find that getting neutral when the bike is moving is just barely flick on the shift lever.